Question

question 10 of 10
what do you know to be true about the values of a and b?
a. a < b
b. a = b
c. a > b
d. cant be determined

Explanation:

Step1: Find the value of \(a\)

The sum of angles in a triangle is \(180^{\circ}\). For the first triangle, \(x + 75+a=180\). Since \(x\) is an angle of a triangle and we assume no other information (but if it's a non - right triangle with angles \(x\), \(75^{\circ}\), \(a^{\circ}\)), if we assume \(x\) is not given but for the sake of comparison (using the property that in a triangle, the larger angle is opposite the longer side, but here we use angle sum). Let's assume \(x\) is such that \(a = 180-(75 + x)\). But if we assume \(x\) is not a right angle. Wait, another approach: the maximum value of \(a\) occurs when \(x\) is minimum (\(x>0\)). The minimum value of \(a\) is \(a>180-(75 + 90)=15\) (if \(x\to90\)). But a better approach: use the fact that in a triangle, the larger angle is opposite the longer side. Wait, no, we can calculate the range. The first triangle: \(a=180 - 75-x=105 - x\). The second triangle: \(b = 180-(60 + y)\). But if we assume \(x=y\) (since no information about \(x\) and \(y\) is given otherwise). Then \(a=105 - x\) and \(b=120 - x\).

Step2: Compare \(a\) and \(b\)

Subtract \(a\) from \(b\): \(b - a=(120 - x)-(105 - x)=15>0\)

Answer:

A. \(a < b\)